imc

Question

In the figure below, 3 of the 6 disks are to be painted blue, 2 are to be painted red, and 1 is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible? FIGURE

Accepted Answer

First we figure out the number of ways to put the 3 blue disks. Denote the spots to put the disks as 1-6 from left to right, top to bottom. The cases to put the blue disks are (1,2,3),(1,2,4),(1,2,5),(1,2,6),(2,3,5),(1,4,6). For each of those cases we can easily figure out the number of ways for each case, so the total amount is 2+2+3+3+1+1 = 12.